Generalized minimax inequalities for set-valued mappings
In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employi...
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Published in | Journal of mathematical analysis and applications Vol. 281; no. 2; pp. 707 - 723 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
San Diego, CA
Elsevier Inc
15.05.2003
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/S0022-247X(03)00197-5 |